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Group Details

Geometric Science of Information

The objective of this group is to bring together pure/applied mathematicians, physicist and engineers, with common interest for Geometric tools and their applications. It notably aim to organize conferences and to promote collaborative european and international research projects, and diffuse research results on the related domains. It aims to organise conferences, seminar, to promote collaborative local, european and international research project, and to diffuse research results in the the different related interested domains.

Machine learning is an interdisciplinary field in the intersection of mathematical statistics and computer sciences. Machine learning studies statistical models and algorithms for deriving predictors, or meaningful patterns from empirical data. Machine learning techniques are applied in search engine, speech recognition and natural language processing, image detection, robotics etc. In our course we address the following questions:
What is the mathematical model of learning? How to quantify the difficulty/hardness/complexity of a learning problem? How to choose a learningmodel and learning algorithm? How to measure success of machine learning?The syllabus of our course:

Jean-Louis Koszul -
(reed) 2019 Springer LINKVideoFlyer
Offers a unique and unified overview of symplectic geometry, Highlights the differential properties of symplectic manifolds, Great interest for the emerging field of "Geometric Science of Information”
This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds. It consists of six chapters: Some Algebra Basics, Symplectic Manifolds, Cotangent Bundles, Symplectic G-spaces, Poisson Manifolds, and A Graded Case, concluding with a discussion of the differential properties of graded symplectic manifolds of dimensions (0,n). It is a useful reference resource for students and researchers interested in geometry, group theory, analysis and differential equations. This book is also inspiring in the emerging field of Geometric Science of Information, in particular the chapter on Symplectic G-spaces, where Jean-Louis Koszul develops Jean-Marie Souriau's tools related to the non-equivariant case of co-adjoint action on Souriau’s moment map through Souriau’s Cocycle, opening the door to Lie Group Machine Learning with Souriau-Fisher metric.

Machine/deep learning is exploring use-cases extensions for more abstract spaces such as graphs, differential manifolds, and structured data. The most recent fruitful exchanges between geometric science of information and Lie group theory have opened new perspectives to extend machine learning on Lie groups. After the Lie group’s foundation by Sophus Lie, Felix Klein, and Henri Poincaré, based on the Wilhelm Killing study of Lie algebra, Elie Cartan achieved the classification of simple real Lie algebras and introduced affine representation of Lie groups/algebras applied systematically by Jean-Louis Koszul. In parallel, the noncommutative harmonic analysis for non-Abelian groups has been addressed with the orbit method (coadjoint representation of group) with many contributors (Jacques Dixmier, Alexander Kirillov, etc.). In physics, Valentine Bargmann, Jean-Marie Souriau, and Bertram Kostant provided the basic concepts of Symplectic Geometry to Geometric Mechanics, such as the KKS symplectic form on coadjoint orbits and the notion of Momentum map associated to the action of a Lie group. Using these tools Souriau also developed the theory of Lie Group Thermodynamics based on coadjoint representations. These set of tools could be revisited in the framework of Lie group machine learning to develop new schemes for processing structured data.

Structure preserving integrators are numerical algorithms that are specifically designed to preserve the geometric properties of the flow of the differential equation, such as invariants, (multi-)symplecticity, volume preservation, as well as the configuration manifold. As a consequence, such algorithms have proven to be highly superior in correctly reproducing the global qualitative behavior of the system. Structure-preserving methods have recently undergone significant development and constitute today a privileged road in building numerical algorithms with high reliability and robustness in various areas of computational mathematics. In particular, the capability for long-term computation makes these methods particularly well adapted to deal with the new opportunities and challenges offered by scientific computations. Among the different ways to construct such numerical integrators, the application of variational principles (such as Hamilton’s variational principle and its generalizations) has appeared to be very powerful, since it is very constructive and because of its wide range of applicability.

An important specific situation encountered in a wide range of applications going from multibody dynamics to nonlinear beam dynamics and fluid mechanics is the case of ordinary and partial differential equations on Lie groups. In this case, one can additionally take advantage of the rich geometric structure of the Lie group and its Lie algebra for the construction of the integrators. Structure preserving integrators that preserve the Lie group structure have been studied from many points of view and with several extensions to a wide range of situations, including forced, controlled, constrained, nonsmooth, stochastic, or multiscale systems, in both the finite and infinite dimensional Lie group setting. They also naturally find applications in the extension of machine learning and deep learning algorithms to Lie group data.

This Special Issue will collect long versions of papers from contributions presented during the GSI'19 "Geometric Science of Information" conference (www.gsi2019.org) but will not be limited to these authors and is open to international communities involved in research on Lie groups machine learning and Lie group structure-preserving integrators.

Prof. Frédéric Barbaresco

Prof. Elena Cellodoni

Prof. François Gay-Balmaz

Prof. Joël Bensoam
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website . Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Two NSF/NIH funded postdoc positions are available in the following fields:

-Computational or applied topology/geometry/graph/algebra

-Machine learning/deep learning

-AI-based drug design and discovery

-Computational biophysics

Ideal candidates should have experience in code development, have demonstrated the potential for excellence in research, and hold a recent Ph.D. degree in either mathematics, computer science, computational biophysics, computational chemistry, or bioinformatics. The selected candidates will be teamed up with top performers in recent D3R Grand Challenges, a worldwide competition series in computer-aided drug design. Salary depends on experience but will be at least $47.5k. The positions enjoy standard faculty health benefit. Please send CV to weig [at] msu.edu.

These projects, financed by WASP (Wallenberg AI, Autonomous System and Software Programme), aim at introducing innovative algorithms and methodologies to overcome the limitations of multi-objective black-box optimization. They are part of a collaboration with Stanford University. The students will be encouraged to apply to the WASP exchange program with Stanford to work closely with collaborators.

Open post-doc position at Géoazur in collaboration with Inria, at SophiaAntipolis, France, in the research area: Curvilinear network detectionon satellite images using AI, stochastic models and deep learning.

To apply, please email a full application to both Isabelle Manighetti
(manighetti[at]geoazur.unice.fr) and Josiane Zerubia
(josiane.Zerubia[at]inria.fr), indicating “UCA-AI-post-doc” in the e-mail
subject.

The application should contain:

a motivation letter demonstrating motivation, academic strengths
and related experience to this position.

CV including publication list

at least two major publications in pdf

minimum 2 reference letters

Project abstract

Curvilinear structure networks are widespread in both nature and
anthropogenic systems, ranging from angiography, earth and environment
sciences, to biology and anthropogenic activities. Recovering the
existence and architecture of these curvilinear networks is an essential
and fundamental task in all the related domains. At present, there has
been an explosion of image data documenting these curvilinear structure
networks. Therefore, it is of upmost importance to develop numerical
approaches that may assist us efficiently to automatically extract
curvilinear networks from image data.

In recent years, a bulk of works have been proposed to extract
curvilinear networks. However, automated and high-quality curvilinear
network extraction is still a challenging task nowadays. This is mainly
due to the network shape complexity, low-contrast in images, and high
annotation cost for training data. To address the problems aroused by
these difficulties, this project intends to develop a novel,
minimally-supervised curvilinear network extraction method by combining
deep neural networks with active learning, where the deep neural
networks are employed to automatically learn hierarchical and
data-driven features of curvilinear networks, and the active learning is
exploited to achieve high-quality extraction using as few annotations as
possible. Furthermore, composite and hierarchical heuristic rules will
be designed to constrain the geometry of curvilinear structures and
guide the curvilinear graph growing.

The proposed approach will be tested and validated on extraction of
tectonic fractures and faults from a dense collection of satellite and
aerial data and “ground truth” available at the Géoazur laboratory in
the framework of the Faults_R_Gems project co-funded by the University
Côte d’Azur (UCA) and the French National Research Agency (ANR). Then we
intend to apply the new automatic extraction approaches to other
scenarios, as road extraction in remote sensing images of the Nice
region, and blood vessel extraction in available medical image databases.